Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C22×D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2309 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C22×D4×C61 | C4 |
| hypercenter | C22×D4 | #6923 |
| hypocenter | C61 | #2309 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
1104 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=g,b^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^11,c^b=ce,h^g=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #30601233, #30601234, #30601241, … |
| maximal normal subgroup of | #30601233, #30601234, #30601241, … |
| maximal quotient of | #30608657, #30608680, #30608699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20983);